nengolib.Alpha

nengolib.synapses.Alpha(tau)[source]

A second-order lowpass: 1/(tau*s + 1)**2.

Equivalent to convolving two identical lowpass synapses together.

Parameters:

tau : float

Time-constant of exponential decay.

Returns:

LinearSystem

Second-order lowpass with identical time-constants.

Examples

>>> from nengolib import Alpha
>>> import matplotlib.pyplot as plt
>>> taus = np.linspace(.01, .05, 5)
>>> for tau in taus:
>>>     sys = Alpha(tau)
>>>     plt.plot(sys.ntrange(100), sys.impulse(100),
>>>              label=r"$\tau=%s$" % tau)
>>> plt.xlabel("Time (s)")
>>> plt.legend()
>>> plt.show()

(Source code)

_images/nengolib-synapses-Alpha-1.png